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Proof step 4 from proof abs-nodes-append-h (previous step)

abs-nodes(buf0, m, x0, lax0, false), ∀ buf, m, x0, lax0, buf1, x1, lax1, weak. # buf < # buf0 → abs-nodes(buf, m, x0, lax0, false) → (abs-nodes(buf + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf, x1, lax1, weak)) ⊦ abs-nodes(buf0 + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf0, x1, lax1, weak)

User applied rule constructor cut

And obtained the following new goals

Proof step 5:
x0 = [], abs-nodes(buf0, m, x0, lax0, false), ∀ buf, m, x0, lax0, buf1, x1, lax1, weak. # buf < # buf0 → abs-nodes(buf, m, x0, lax0, false) → (abs-nodes(buf + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf, x1, lax1, weak)) ⊦ abs-nodes(buf0 + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf0, x1, lax1, weak)
Proof step 10:
x0 = nd + x, abs-nodes(buf0, m, x0, lax0, false), ∀ buf, m, x0, lax0, buf1, x1, lax1, weak. # buf < # buf0 → abs-nodes(buf, m, x0, lax0, false) → (abs-nodes(buf + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf, x1, lax1, weak)) ⊦ abs-nodes(buf0 + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf0, x1, lax1, weak)

Rule argument

var: x0

Additional information

Used simplifier rules: list freely generated by [], +;;